Notes - Linear Algebra I MT22, Chapter 6

Created: December 31, 2022

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• [[Course - Linear Algebra I MT22]]^U
  • [[Notes - Linear Algebra MT23, Rank-nullity theorem]]^U
• Content covered:
  • Prove a linear map is invertible if and only if it is bijective (Prop. 154)
  • Prove there exists an invertible linear map between two finite dimensional vector spaces if they have the same dimension. (Prop. 156)
  • Prove lots of properties about the kernel and image relating to subspaces (Prop. 159)
  • Prove the rank nullity theorem (The. 162).

Flashcards

What’s the useful inequality about the nullity composition of two linear maps?

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$$\text{null}(ST)\le \text{null}(S)+\text{null}(T)$$

What’s the useful inequality about the rank of the sum of two linear maps?

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$$\text{rank}(S+T)\le \text{rank}(S)+\text{rank}(T)$$

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